Uniform disk lying on a flat, frictionless surface

[QwertyXP]

A uniform disk is lying on a flat, frictionless surface, and a force is applied as shown:
http://www.freeimagehosting.net/uploads/ae622047b5.jpg

What will be the motion of the disk.. more importantly, the motion of center of mass of the disk. will it move in a straight line, or will it move in a slanting direction towards the right?

 

[mgb_phys]

If this is a homework question - you have to make an attempt at an answer.
If this is a 'in the pub' discussion - search for threads on a ball rolling on a frictionless surface, this is basically the same thing.

 

[Naty1]

Draw a radial line from the point of application of the force thru to center of the disk...that will give you an idea how your force is actually a torque...your force can then be decomposed into a vertical component and a component thru the center of the disk along the radial line...your question is hence answered.

 

[Doc Al]

What will be the motion of the disk.. more importantly, the motion of center of mass of the disk.

The acceleration of the center of mass is given by Newton's 2nd law.

 

[QwertyXP]

@Naty1:
Before posting here, i tried solving this the way u said. But I guess if we decomposed the force, one of the components would be tangential to the circle at the point of contact (not vertical). And the other, as u said, would be through the center of the disk along the radial line.

However, in that case, the component through the centre of disk would cause it to move in a sideways direction... wouldn't it? The acceleration of the center of mass would then not be in the same direction as force applied.

Let's look at another example.. i might somehow understand the above question if i get the answer to the following: if an impulse were applied tangential to the disk (dt -->0), would it simply rotate or would it also move forward? Is the angular velocity calculated using angular momentum?

 

[Doc Al]

if an impulse were applied tangential to the disk (dt -->0), would it simply rotate or would it also move forward?

What do you think? Newton's 2nd law still applies.

Is the angular velocity calculated using angular momentum?

Yes. An angular impulse about the center of mass will create a change in angular momentum.

 

[rcgldr]

A force is applied as shown ...

You didn't specify if there was friction at the point of application of the force. If friction is zero at the point of application of force, then there are no rotational effects due to the force. If the friction is non-zero at the point of application of force, then the disk experiences angular acceleration as well as linear acceleration.

 

[cesiumfrog]

The OP's diagram is very similar to a problem that (alarmingly) many physicists and physics teachers get wrong (as demonstrated at the recent AIP conference), namely "what is the trajectory of a rocket if the nozzel is bent 90 degrees?".

 

[russ_watters]

You didn't specify if there was friction at the point of application of the force. If friction is zero at the point of application of force, then there are no rotational effects due to the force. If the friction is non-zero at the point of application of force, then the disk experiences angular acceleration as well as linear acceleration.

I think we must assume there is friction (or a structure to make contact with), otherwise it isn't possible to apply the force as shown.

 

[rcgldr]

You didn't specify if there was friction at the point of application of the force. If friction is zero at the point of application of force, then there are no rotational effects due to the force. If the friction is non-zero at the point of application of force, then the disk experiences angular acceleration as well as linear acceleration.

I think we must assume there is friction (or a structure to make contact with), otherwise it isn't possible to apply the force as shown.

Russ is correct, the direction of the force implies that there must be friction. Not clear is what happens to the direction of the force once the disk starts moving.

Regarding the rocket with a sideways nozzle, there's a type of fireworks called a buzz bomb that is essentially a rocket with a sideways nozzle and small wings. This is a video of a small 2 stage buzz bomb:

http://www.youtube.com/watch?v=GXlXCGGTG9A&fmt=18

Another one, in day time:
http://www.youtube.com/watch?v=Nn9cA4D-2ss&fmt=18